Iterated Majority Voting

Abstract

Abstract. We study a model in which a group of agents make a sequence of collective decisions on whether to remain in the current state of the system or switch to an alternative state, as proposed by one of them. Examples for instantiations of this model include the step-wise refinement of a bill of law by means of amendments to be voted on, as well as resource allocation problems, where agents successively alter the current allocation by means of a sequence of deals. We specifically focus on cases where the majority rule is used to make each of the collective decisions, as well as variations of the majority rule where different quotas need to be met to get a proposal accepted. In addition, we allow for cases in which the same proposal may be made more than once. As this can lead to infinite sequences, we investigate the effects of introducing a deadline bounding the number of proposals that can be made. We use both analytical and experimental means to characterise situations in which we can expect to see a convergence effect, in the sense that the expected payoff of each agent will become independent from the initial state of the system, as long as the deadline is chosen large enough.

Introduction to Computational Social Choice

“…Brânzei et al (2013) studied the price of anarchy of such iterated voting processes for several rules. A different iterative model was studied by Airiau and Endriss (2009), where in each step a voter is randomly selected, proposes a new alternative as a challenger to the current winning alternative, and the voters have to choose between the two.…”

Strategic Voting

“…Other models assume backward induction reasoning and analyze subgame perfect equilibria. This can apply when voters sequentially vote on parts of the decision [17], [33], [72], or when they have repeated opportunities to offer new candidates that will compete with the current winner [1].…”

“…This review paper is a hyper-condensed version of a book on strategic voting that is forthcoming this year. 1 The main purpose of the book is to overview the main approaches to strategic voting, in a way that makes these approaches comparable across fields and disciplines. In this paper I will mention the main directions and lines of work, but almost without going into the technical details.…”

Acyclic Games and Iterative Voting

“…Specifically, some of this previous work has been devoted to the analysis of solution concepts such as elimination of dominated strategies [Dhillon and Lockwood, 2004] and strong equilibria [Sertel and Sanver, 2004]. There has been other multi-step voting procedures that have been proposed in the literature, such as iterated majority vote [Airiau and Endriss, 2009] and extensive form games where voters vote one by one [Desmedt and Elkind, 2010]. In contrast to iterative voting, these models are inconsistent with the better-reply dynamics in normal form games, and are analyzed via different techniques.…”